# Linear and Non-linear similarity of matrices

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Yangyang Li, Princeton University
Fine Hall 314

In-Person Talk

Two n-by-n real matrices A and B are linearly similar if there is a non-singular n-by-n real matrix Q so that $B = QAQ^{-1}$. In general, one can consider $\phi$ to be a homeomorphism of $R^n$ to itself, and if $B = \phi A \phi^{-1}$ holds as maps, A and B are said to be topologically linear (non-linearly similar). In this talk, we will discuss the relationship between these two similarities as well as their applications.